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Modeling Interfacial Tension of Hexane \(+\) Alcohol Mixtures at Different Temperatures Using Linear Gradient Theory with Cubic Plus Association Equation of State

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Abstract

This work has been dedicated to modeling the interfacial tension of hexane \(+\) alcohol mixtures in the temperature range of 283.15 K to 313.15 K. The cubic plus association equation of state is applied to the liquid–vapor phase equilibrium calculations. The binary interaction parameters are obtained according to the experimental phase equilibrium data. The linear gradient theory is used as a predictive and adjustment approach to describe the interfacial tension of hexane \(+\) alcohol mixtures. The influence parameters of the pure components were correlated with the temperature and the symmetric parameters were correlated with the temperature and with the carbon number of the alcohol. The results of this work show that the equation of state used is capable of simultaneously representing the phase equilibrium and interfacial tension of the mixtures studied. Despite using the simplified version of the gradient theory, the results obtained in the interfacial tension are in agreement with those published in the literature.

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Abbreviations

P :

Absolute pressure

T :

Absolute temperature

\(a_0\) :

Adjustable parameter of the CPA-EOS

\(c_1\) :

Adjustable parameter of the CPA EOS

A :

Adjustable parameter of the influence parameter

B :

Adjustable parameter of the influence parameter

a :

Attractive parameter in CPA-EOS

b :

Covolume parameter in the CPA-EOS

\(f_0\) :

Helmholtz energy density

c :

Influence parameter

\(k_{ij}\) :

Interaction parameter in the CPA-EOS

x :

Mole fraction of the liquid phase

C :

Number of carbons in the alcohol

\(n_c\) :

Number of components

n :

Number of points

z :

Position in the interface

AAD :

Statistical deviation

\(X_{A_i}\) :

The mole fraction of the molecule i not bonded at site A

g :

The radial distribution function

R :

Universal gas constant

\(\mu \) :

Chemical potential

\(\Omega \) :

Grand thermodynamic potential

\(\sigma \) :

Interfacial tension

\(\rho \) :

Molar concentration

\(\eta \) :

Reduced density

\(\beta _{ij}\) :

Symmetric parameter

\(\epsilon ^{A_i B_i}\) :

The association energy

\(\Delta ^{A_i B_j}\) :

The association strength

\(\beta ^{A_i B_i}\) :

The association volume

c :

Critical condition

i, j, s :

Species

0:

Equilibrium condition

exp :

Experimental

L :

Liquid phase

theo :

Theoretical

V :

Vapor phase

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Acknowledgements

A.H acknowledges the economic support given by the UCSC.

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  1. Facultad de Ingeniería, Universidad Católica de la Santísima Concepción, Alonso de Ribera 2850, Concepción, Chile

    Ariel Hernández

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Hernández, A. Modeling Interfacial Tension of Hexane \(+\) Alcohol Mixtures at Different Temperatures Using Linear Gradient Theory with Cubic Plus Association Equation of State. Int J Thermophys 41, 125 (2020). https://doi.org/10.1007/s10765-020-02703-x

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